I can only give my initial first impressions as I have only had the S4 about a day. Please remember these are only MY thoughts, not saying you will agree or not.
If anyone is switching from an iPhone, Samsung has made it super easy with their smartswitch website. In minutes my contacts, calender, memos, sms, pics, music and videos were copied to the S4. The only bad thing was everything was copied to the internal memory not the SD card. So the music and pictures I ended up deleting and readding myself to the SD card.
The iPhone 5 is a very solid and well made phone and even though smaller than the S4 it feels a lot heavier as its so dense and hard. This does not make the S4 feel cheap like I see in some reviews as the S4 is amazingly light for its size and not as hard so I think that's why some think its cheap feeling.
Both have really nice screens but I give the edge to the S4 as it seems more colorful and of course the huge screen.
I have the OS split. I give the edge to the iPhone 5 as its just so smooth and the keyboard seems more accurate for me at least. The S4 wins hands down on the sheer number of features and tweaks you can do.
Now to the 16gb storage talks. My S4 has 16gb internal with a 64gb sd card and my iPhone 5 has 64gb internal. Once all my music, pics and videos were copied to the S4 sd card and I added most of the same apps (93 apps are on my S4) I had on my iPhone 5, I have 5.5gb internal free. Approx the same music and apps are on my iPhone 5 and I have 7gb free.
I do not think the 16gb internal limit will effect the majority of us. I have every app (93 of them) I use a lot and pics/vids/music on the sd card and still have room to spare. I admit only about 10 games like Angry Birds, Blood/Guts, few flying ones and no really massive ones but I can still easily fit some if I wanted.
My final thoughts are still out on which I will prefer for day to day activities, so I need to give it some time.
I need to say that when outside, the S4 is way more washed out and harder to see than the iPhone 5 screen. I could not imagine trying to read a book on it but general use was fine.
The camera on the S4 is also much better. Besides many more features and settings the pictures come out stunning. The iPhone 5 takes nice pictures too but not quite as good.